Question

1. A commercial airliner is flying at 450 mph, 20° east of north, relative to the surrounding air. The surrounding air though is blowing at 90 mph, 40° south of east, relative to the ground. The relative humidity of the air is 70%. How fast is the airliner flying relative to the ground, and in what direction?

2. Kenny and Cartman are playing paintball blindfolded. They are initially standing back-to-back, facing away from each other. Treat it as if they are standing on exactly the same spot. Kenny then runs 8 meters due west. Meanwhile, Cartman runs 2 meters due east, turns left, and runs 6 meters 30° east of north. They then turn around and start shooting paintballs. Of course, they are both blindfolded, so they aren’t coming anywhere close to hitting each other. How far apart are they when they start shooting?

3. Cartman decides to cheat, and peaks through his blindfold to see where Kenny is. He then turns and aims at Kenny. What direction does he need to aim in to hit Kenny? (relative to the cardinal axes, i.e. something like 40° south of west)

Answer 1

1. 428 mph, 59 degree North of East.

2. 14 m

3. 68 degrees west of south. Or 22 degree south of west.